Trumka, the bulb-nosed, bristle-mustached president of the AFL-CIO, is sitting in a conference room at the union's headquarters in Columbus, where he has come to fire up the troops in advance of the presidential election.

Here's the joke: A man sees a sign by the side of the road reading, "Republican puppies, $50." He stops for a look, but he's headed out of town and can't take one. Six weeks or so later, he passes by again. This time, the sign reads "Democrat puppies, $100."

"He stops and looks and he says, 'Wait a second, these are the same puppies,'" Trumka says, jabbing a stubby forefinger for emphasis. "And the guy says, 'Yeah, but now they have their eyes open.'"

To Trumka, the joke has a kernel of truth: People will vote the right way, he tells me -- but only after you open their eyes to the things they need to know.

President Obama, you may have heard, appears to be in good shape to win Ohio and other Rust Belt states on Tuesday, in large part due to white working-class voters' distrust of his opponent, Mitt Romney. But that impression didn't take hold on its own, nor was it the sole creation of the Obama campaign. It had a lot of help from Trumka and his minions.

"A year ago, all the talk was Obama could never win with high unemployment," the AFL-CIO's political director, Mike Podhorzer, wrote in a recent memo. "The early conventional wisdom went further, writing off working class voters, asserting that the only path available to President Obama was upscale voters in states like North Carolina." Instead, the demographic that should have been Obama's greatest weakness may be the one that saves the election for him.

Indeed, if the manufacturing states of the Upper Midwest end up forming a surprising electoral-vote firewall for Obama, insulating his reelection bid from potential losses in Florida, Virginia, and Colorado, he will owe a debt of gratitude to the unions, who have been working doggedly, and largely under the radar, on his behalf. In the last four days of the presidential campaign, the AFL-CIO says its 128,000 volunteers will have knocked on 5.5 million doors, made 5.2 million phone calls and passed out 2 million leaflets in six targeted states. In Ohio alone, the union has 20 staging areas from which to make those calls and send crews out to knock on doors.

On Saturday morning, Tim Burga, the wiry president of the Ohio AFL-CIO, stood under an alphabet soup of signs, unions being second only to the military in their zeal for acronyms: AFSCME for Obama-Biden, NATCA, TWU, AFT, UFCW. Like a boxer entering the ring, he had taken off his mustard-colored work jacket, revealing a black IUPAT tee beneath.

"We've been active for a good long time now," Burga said. "We need to leave it all on the field now for the next four days. Walk till our feet are hurting. Talk till our throats are scratchy. Go to the work sites, pull every last vote out that we can pull out." The 40 or so union members in the low-ceilinged back room, a group long on pot bellies and mustaches, nodded approvingly. There was also a woman in a T-shirt reading "Kicking Ass for the Working Class."

"And when we do that," Burga continued, "we're going to say to America: 'Ohio won this election! Labor won this election, and we did it for the working people!' Are you with me?" "Yeah!" the group shouted.

The unions' effort is much bigger than four years ago, Trumka says, because of the campaign-finance changes stemming from the Citizens United decision of the Supreme Court, which made it legal for unions to engage in political communication with the general public, not just their own members. "Trust me, it's a horrible, horrible thing, and it's corrosive to democracy," Trumka says of Citizens United. "The only good thing it did is, it gave us the ability to do a super PAC so that we could talk to nonunion workers."

The organizing effort in Ohio got a jumpstart a year ago, when the state's Republican governor, John Kasich, attempted to pass changes to collective-bargaining rights. Labor revolted against the legislation, known as Senate Bill 5, and staged a referendum to repeal it that ended up passing with 62 percent of the vote. The success of that effort laid the groundwork for this year's political mobilization on behalf of Obama, Senator Sherrod Brown (who is also favored to win, despite having tens of millions spent against him by the Chamber of Commerce and other interest groups), and other Democrats.

"Trust me, Citizens United is a horrible, horrible thing, and it's corrosive to democracy," Trumka says. "The only good thing it did is, it gave us the ability to do a super PAC."

I spent a couple of hours Saturday afternoon walking a mixed-race, working-class neighborhood on the east side of Columbus with Diana Vernon, a sunny 51-year-old head cook for a suburban school district. Canvassing is thankless work -- hours on your feet, trudging from door to door to remind people to vote, almost none of whom are home -- yet Vernon does it almost every weekend, and last week spent a full day in the rain distributing literature for a union-backed ballot measure.

"Some of my coworkers are voting for Romney," Vernon admitted. "I'm like, 'How can you? You're a regular working person. You're a lunch lady!' But a lot of it is social issues."

When the canvassing gets discouraging, Vernon thinks back to the SB5 fight. "A lot of people got out and worked really hard, and I really do think we made a difference," she said. "I just think you've got to stand up for what you believe in."

In polls, and in my own conversations with Ohioans, there's a clear sense that Romney is viewed as out of touch with the working class of this acutely class-conscious, industrial state, of which old-line unions still form the backbone. Back at the union hall, I ask Trumka how much of that perception the union can take credit for.

Trumka laughs heartily, his brown eyes squinting. "Look, Romney did that," he says. "Romney doesn't have a clue what working people are going through. Now, did we point that out to a lot of people? Absolutely, because it's something they need to know." According to the union's research, among the people it reached, its messaging caused Romney's support to drop 30 points among white males and 50 points among born-again Christians. That's the moral of the puppy joke.

Though they are working in lockstep today, unions and Obama have not always been the happiest of political bedfellows. The Employee Free Choice Act, the legislation commonly known as card check that labor had hoped would be the reward for its $400 million investment in the 2008 election, fizzled early in Obama's term. From antagonizing the teachers unions to staging this year's Democratic convention in a right-to-work state, the president has frequently frustrated his erstwhile union allies.

"Democrats are not the labor party; they're the party we have to rely on," Bruce Bostick, the mustached manager of the Ohio steelworkers' retiree fund, tells me. He's wearing faded jeans, a beret, and a vintage Sherrod Brown for Congress button from 1996, speckled with rust. "Frankly, I think labor as a movement has dropped the ball," Bostick adds. "We didn't build a movement on the outside to hold the Democrats' feet to the fire. So we got a convoluted health-care bill, no national jobs program, and a stimulus nobody understood."

Despite such rumblings of dissatisfaction, there's one major force keeping labor on Obama's side: the Republican Party, which, Trumka says, has adopted "the most anti-worker, anti-union platform of any major party in the history of the United States. It's mobilized us, it's energized us, it's brought us together with more solidarity than we've had in years."

The conundrum, for the unions, is ensuring they don't get taken for granted when and if Obama does win a second term. Now that victory is in sight, Trumka wants to make it clear that labor plans to collect what they feel they are owed.

"Look, we've laid some markers down," he says. "No tax cuts for the rich, not an extension of those tax cuts, not one minute. Two, no cuts in benefits for Social Security, Medicare and Medicaid. And we'll fight for those things. We'll fight no matter who proposes them. If a Democrat proposes them, we'll go after them as well."

But can labor credibly threaten the Democrats, given that they have nowhere else to go? "Of course we have an option," Trumka says. "It's real simple. There's things called primaries." He pauses to let this threat sink in.

"If they're voting against what the people want, it'll cost them. It'll cost them big time," he adds. "No one will be immune. We're going to hold people accountable."

I note that Trumka hasn't mentioned card check, or as he prefers to call it, "labor law reform." But he denies the union has given up on that priority.

"Never. You'll see it," he says. "That's within the next term." How is that possible, without a Democratic House of Representatives or 60 votes in the Senate? Trumka smiles. His eyes twinkle.

"There's another election between now and then," he says. And the AFL-CIO isn't going anywhere.